Yes indeed we see Paul baptizing others in Acts.
And again, yes the verses I quoted from are from the letter to the Corinthians, as far as my further commenting, I am also speaking of other verses found in 1 Corinthians
Heres all the verses I had just mentioned in brief
1Cr 1:12 Now this I say, that every one of you saith, I am of Paul; and I of Apollos; and I of Cephas; and I of Christ.
1Cr 1:13 Is Christ divided? was Paul crucified for you? or were ye baptized in the name of Paul?
1Cr 1:4 I thank God that I baptized none of you, but Crispus and Gaius;
1 Cr 1:15 Lest any should say that I had baptized in mine own name.
1 Cr 1:16 And I baptized also the household of Stephanas: besides, I know not whether I baptized any other.
Here as well,
1Cr 3:4 For while one saith, I am of Paul; and another, I am of Apollos; are ye not carnal?
1 Cr 3:5 Who then is Paul, and who is Apollos, but ministers by whom ye believed, even as the Lord gave to every man?
1 Cr 3:6 I have planted, Apollos watered; but God gave the increase.
1 Cr 3:7 So then neither is he that planteth any thing, neither he that watereth; but God that giveth the increase.
So all in the same epistle there.
God bless you